If your binoculars keep vanishing from the hook by the door, that's a good sign, and the simplest gift is a pair of their own.
Start with exit pupil, which is aperture divided by magnification. A 10×50 gives a 5 mm beam. That's bright enough for the Pleiades and the Moon's craters, and it's the size most adult guides start with. For smaller hands, try the pair before you buy it: a 50 mm binocular can feel heavy after a few minutes, and a kid who can't hold it steady won't use it. Our binocular guide explains the numbers.
Add a sky book or chart so the binoculars have somewhere to point. Turn Left at Orion is built around what you actually see in a small instrument, which suits a beginner. Add a dim red light so they can read the page without losing their dark adaptation.
Skip the toy-store telescope promising 600× magnification. Magnification isn't what limits a small instrument, and a shaky, dim view puts kids off. Binoculars and a book they use every clear night beat a telescope that stays in its box.
For the short list we'd start with, see the Starter Kit.